Virtual Source Array-Based Multiple Time-Reversal Focusing

Heechun Song,Jeasoo Kim,Gihoon Byun

doi:10.3390/app8010099

Abstract

Time reversal (TR) is the process of generating a spatio-temporal focus at a probe source (PS) location by transmitting a time-reversed version of a received signal. While TR focusing requires the PS for a coherent acoustic focus at its origin, the requirement of the PS has been partially relaxed by the introduction of the concept of a virtual source array (VSA) (J. Acoust. Soc. Am. 2009, 125, 3828–3834). A VSA can serve as a remote platform or lens and redirect a focused field to a selected location beyond the VSA for which the field is assumed as a homogeneous medium with constant sound speed. The objective of this study is to extend VSA-based single TR focusing to simultaneous multiple focusing. This is achieved using the optimization theory by employing the multiple constraints method derived from a constraint matrix, which consists of appropriately synchronized transfer functions. Through numerical simulations, it is found that simultaneous multiple focusing can be achieved with distortionless response at selected multiple locations, and its performance degrades in the presence of sound speed mismatch. For achieving robust multiple focusing in the mismatch environment, singular value decomposition is applied to obtain the weight vector (i.e., backpropagation vector) that best approximates the column vectors of the constraint matrix. Numerical simulation results show that VSA-based multiple TR focusing using SVD is not a method to simultaneously focus on multiple locations, but a method of constructing a field which robustly passes through multiple locations in sound speed mismatch environment.

Highlights

Over the last several decades, time reversal (TR) processing has been extensively studied in various fields [1,2,3]
In TR processing, a transmitted probe signal is received at an array of source-receive elements, which is referred to as a time-reversal mirror (TRM), and the received signal is time reversed to be backpropagated into the medium
The objective of this study is to extend the virtual source array (VSA)-based single TR focusing to simultaneous multiple focusing at arbitrarily selected locations

Summary

Introduction

Over the last several decades, time reversal (TR) processing has been extensively studied in various fields [1,2,3]. If the propagation medium is static, TR processing results in coherent acoustic focusing (or pulse compression) at the probe source (PS) location where the signal was generated. One of the main advantages of TR processing is generating a focused field without a-priori knowledge about the propagation medium (i.e., self-adaptive) because of the TR invariance of the wave equation. The adaptive time-reversal mirror (ATRM), proposed by Kim et al [4], backpropagates the weight vector obtained as the optimal solution of an objective function with a single imposed constraint. It can focus distortionless response at a single location while simultaneously forming nulls by minimizing the total reception power at different arbitrary locations. The ATRM can be applied directly to selective focusing on a weak target [4] and to underwater multiuser communications to mitigate cross talk [5]

Objectives

Methods

Conclusion